After reading through the many messages posted here so far, I have a few observations, as well as a few questions.
Several posters have mentioned vinyl LPs, and tapes. It's important to remember the distinction between analog and digital characteristics. Unlike digital, analog recording *always* introduces some degree of distortion. This may or may not be terribly important if you're backing up alphanumeric data, but it can make a huge difference for audiovisual data. Yes, both an LP and a commercial DVD are mechanically pressed, but even under the best storage conditions an LP collects dust in its grooves, and even the best playback needle and arm will cause wear in the grooves, with the result that sound inevitably degrades slightly with each use.
Tape is a magnetic medium. Each time a tape is played, a slight amount of the magnetized oxide coating wears off onto the heads and rollers, again introducing some degradation. Tape is also subject to some amount of print-through, especially with longer--and thus thinner--tapes, where the magnetism "migrates" through its backing onto the layers above and below it. Further, it's possible for tape to stretch slightly. And finally, any external source of magnetism can degrade or destroy the data, depending on its strength and proximity.
With both of these types of analog media you will retain the basic information recorded, but with each playback, and also merely with the passage of time, more and more distortion and degradation of signal will be introduced. This may not be particularly noticeable on an original audiocassette or VHS played on excellent and well-maintained equipment, but distortion becomes immediately apparent if you ever try dubbing a second- or third-generation tape.
Unlike analog media, individual bits of a digital recording are either there, and readable, or they aren't. Virtually every digital recording scheme incorporates an error-correction protocol, so that individual bad bits are corrected in playback. If error-correction gets wiped out you may lose a section of data, or your player may skip or hang (or refuse to load), but uncorrupted data will retain exactly the same quality of information that was originally encoded. Some DVD or CD players are very sensitive to problem areas, while others can be much more forgiving. Commercially pressed DVDs are always far more stable than home-burned discs, but they can have problems if the original pressing was done less than expertly; occasionally you may run across a movie where every copy skips or hangs in the same place.
Thanks to error-correction, most minor scratches on a commercial DVD are ignored by a player. I frequently borrow movie DVDs from my local library or a rental service, and finding a pristine disc is a rarity. Library discs in particular tend to be ill-used, with multitudes of scratches, as well as fingerprints, food, snot, etc. A little water or Windex takes off the foreign matter, and a very finely-abrasive cleaner such as Brasso used with a clean soft cloth will usually tidy up all but the worst scratches. In any case you must always wipe or rub back and forth in a center-to-edge direction--you can rub quite firmly if needed--but *never* around the disc in the direction of play. A random scratch that isn't too deep or too broad will usually spare the error-correction bit, but even a barely visible scratch in the direction of play can easily wipe it out. This kind of scratch is nearly always caused by a portable player being jiggled while playing, or even worse, in a moving vehicle.
Returning to the question of home-burned discs, I have no idea of the longevity that can be expected, but many of the suggestions already made make eminently good sense. Make multiple backups of critical data, if possible no more than second-generation copies from original media, or in any case using as few generations as feasible, always after first verifying the integrity of the source. Use different types of media: CDs or DVDs, external harddrive, flash, online data storage, tape, paper, whatever--including offsite storage--none will always be foolproof. Buy the best discs available for the level of security you need, which may or may not be gold film. Use the best and most reliable CD/DVD writer you can find, and replace it if and when it starts to make errors--I've thrown away two crappy Lite-On drives, and now use either an internal Optiarc or an external HP, either of which is good enough for my purposes. Use well-regarded writing software; I use VSO CopyToDVD, which again suits my own needs. The lower you set the write speed, the fewer write errors are likely to occur. Before writing, inspect each disc for visible dust specks, but try never to touch the play surface with your fingers. Avoid any source of possible vibration while writing, including, as mentioned by one poster, any loud sound. Immediately after writing each disc, verify its playback, preferably in a different drive (or player). Store discs in a dark, dry, cool (not cold) dust-free place, each in its individual pouch.
I've never specifically looked for the recommended Taiyo Yuden discs, but have long used Verbatim DVD+R, which carry a "lifetime warranty"--over the years I've gotten a very few coasters, but never enough to mess around with the warranty. I've given up on other brands, which tended to give a much higher rate of coasters. I've also given up trying to use 8.5 GB double-layer discs, of any brand at all. I've found that when writing VOB files, a reasonable amount of data compression does not noticeably affect audiovisual quality, but disc menus do not like to be compressed, so I nearly always omit them. As far as I'm aware, none of the Verbatim 4.7 GB discs I've written over the past six years have degraded in any way.
A couple of questions:
Someone earlier suggested using DVD-R discs, and I wonder if that was meant to exclude DVD+R; and if so, why?
And someone else cautioned against writing anything directly onto the label side of a disc. I've never tried using LightScribe, and I know better than to put any sort of sticky label onto a disc, so I simply write on it with a Sharpie Fine Point permanent marker. Is there any reason not to do this? In fact I've occasionally erased markings with isopropanol applied with a Q-tip, and so far haven't noticed any playback problems with these discs.